Consistent 10km improvement

I am hoping you can give me a bit of help. I have been running consistently for the past 5 years and I am looking to progress my 10km pb and have an ultimate goal of reaching a sub 35mins (currently 39:02 - splits below). I know this is a massive step up from where I'm at, however, I am not too fixated on the time, ultimately, I just want to find my running limit!

I've had a good look at the 35min program and I'm happy to get stuck straight into it! Just not sure where to start, I did my long run on Sunday and 5*2ks on Tuesday, so what day would you suggest to slot in to/pace etc.?

Also, I have a 10k race on Sunday, 11th July, so just about 2.5 weeks to go.
It's a good flat course, so hopefully the weather will play it's part

I hope your keeping well. How is weather in Sweden, Melbourne is grey, cold and windy, but still ok for running!

Training is going pretty well at the moment, I decided to swap sessions to bring me inline with the program. Therefore, day 1 + 3 were reversed, but all other sessions were on the designated day. Make sense?

Just a few questions:
Should I aim for 15km or 1hr tomorrow?
For Saturday's 5km paced run, what should I be looking to do?
Finally, the easy paced sessions, I have aimed to keep these between 30 - 60 seconds slower than current 10k pace, is this correct?

I have a local 10k race on Sunday 11th July. Looking forward to it and would like to dip under 39mins this time. I was thinking to try and hold 3:50 pace from the start, although, 2k reps avg was 3:53, so maybe pushing a little bit, what do you think?